Space of modular forms of level 30, weight 2, and Character 30.e

• Label: 30.2.e
• Level: $30$
• Weight: $2$
• Character orbit: 30.e
• Rep. character: $\chi_{30}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(30, [\chi])\).

	Total	New	Old
Modular forms	20	4	16
Cusp forms	4	4	0
Eisenstein series	16	0	16

Trace form

4 * q - 4 * q^3 - 4 * q^6 - 4 * q^7 + 4 * q^10 + 4 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^18 + 8 * q^21 - 4 * q^22 - 16 * q^25 - 4 * q^27 - 4 * q^28 - 12 * q^30 - 8 * q^31 - 4 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 + 4 * q^42 + 24 * q^43 - 8 * q^45 + 16 * q^46 + 4 * q^48 - 8 * q^51 + 12 * q^55 - 16 * q^57 - 20 * q^58 - 4 * q^60 - 24 * q^61 - 4 * q^63 + 8 * q^66 - 16 * q^67 + 4 * q^70 - 8 * q^72 - 20 * q^73 + 28 * q^75 + 16 * q^76 + 28 * q^81 - 16 * q^82 + 8 * q^85 + 20 * q^87 - 4 * q^88 + 8 * q^90 + 8 * q^93 + 4 * q^96 + 12 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(30, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
30.2.e.a	$30$	$2$	30.e	15.e	$4$	$4$	$2$	$0.240$	\(\Q(\zeta_{8})\)	None		✓	✓	✓	30.2.e.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)